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  4. If A and B are two matrices such that AB = B and BA = A, then A2 + B2 equals

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Q. If $A$ and $B$ are two matrices such that $AB = B$ and $BA = A$, then $A^2 + B^2$ equals

WBJEEWBJEE 2015

Solution:

Given, $A B=B$ and $B A=A$
Now, $A^{2}+B^{2} =A \cdot A+B \cdot B$
$=A(B A)+B(A B)=(A B) A+(B A) B$
$=B A+A B=A+B$